I played through the game twice this week - first on hard mode, then again on normal mode to pick up the rest of the achievements and was interested to see that some of the puzzles have different solutions.

One obvious difference is that the cheat button is disabled by default on hard mode (a good thing too - I abused it far too much in the original after I accidentally discovered it), though it can be enabled via settings. I can't say whether normal mode offered any extra hints - I was skipping all the dialogue on my second playthrough to get the achievements as fast as possible.

Here are the differences I noticed - I'm trying to remain vague in the descriptions to avoid spoiling them for anyone who hasn't played yet. Did I miss any?

Chapter 1- Gunpowder is readily available on normal mode

Chapter 2- Knitting puzzle pre-solved on normal mode

Chapter 3- Baby Critter puzzle skips a step in normal mode (and I daresay this contributes to the Baby Olympics achievement being so rare as it would be impossible to get on a single normal mode playthrough)- A different item is used at one point inside the submarine